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26 Dec 2012, 05:18
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:27) correct
33%
(01:19)
wrong
based on 5184
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What is the value of x + y in the figure above?
(1) w= 95
(2) z = 125
Attachment:
Angles.png [ 8.38 KiB | Viewed 89228 times ]
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26 Dec 2012, 05:23
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What is the value of x + y in the figure above?
Sum of Interior Angles of a polygon is \(180(n-2)\) where \(n\) is the number of sides (so is the number of angles). So, the sum of the interior angles of a quadrilateral is 180*2=360. Look at the diagram below:
According to the above: (180-x)+(180-y)+(180-z)+(180-w)=360 --> x+y=360-w-z, so all we need to know is the values of w and z.
(1) w= 95. Not sufficient.
(2) z = 125. Not sufficient.
(1)+(2) Sufficient.
Answer: C.
Attachment:
Angles2.png [ 9.97 KiB | Viewed 84229 times ]
Updated on: 14 Jan 2021, 08:27
Originally posted by BrentGMATPrepNow on 01 Sep 2017, 15:09.
Last edited by BrentGMATPrepNow on 14 Jan 2021, 08:27, edited 3 times in total.
Last edited by BrentGMATPrepNow on 14 Jan 2021, 08:27, edited 3 times in total.
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Walkabout
Target question: What is the value of x + y?
Statement 1: w = 95
Important: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value. This concept is discussed in much greater detail in the second video below.
If w = 95, then the angle inside the quadrilateral must be 85.
So, those 2 angles (95 and 85) are "locked." In other words, the 2 lines that create those two angles are locked in place to create the 95- and 85-degree angles.
However, line1 is not locked into place, so we can still move it, which means we can freely alter the size of angle y.
As such, the value of x + y will vary.
Since we cannot answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: z = 125
If z = 125, then the angle inside the quadrilateral must be 55.
Since line2 is not locked into place, we can still move it, which means we can freely alter the size of angle x.
As such, the value of x + y will vary.
Since we cannot answer the target question with certainty, statement 2 is SUFFICIENT
Statements 1 and 2 combined:
We now have the following:
Since all angles in a quadrilateral add to 360 degrees, we know that 85 + 55 + j + k = 360
If we solve for j + k, we get: j + k = 220
Also notice that, since angles x and k are on a line, it must be true that x + k = 180.
Similarly, it must be true that y + j = 180
If we combine both of these equations, we get: x + y + j + k = 360
Since we already know that j + k = 220, we can replace j + k with 220, to get:
x + y + 220 = 360
This means x + y = 140
Since we cannot answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
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